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Two regularization methods for a Cauchy problem for the Laplace equation. (English) Zbl 1132.35493
Summary: A Cauchy problem for the Laplace equation in a rectangle is considered. Cauchy data are given for $y=0$, and boundary data are prescribed for $x=0$ and $x=\pi$. The solution is sought for $0<y\leqslant 1$. We propose two different regularization methods for the ill-posed problem based on separation of variables. Both methods are applied to find regularized solutions which are stably convergent to the exact one with explicit error estimates.

##### MSC:
 35R25 Improperly posed problems for PDE 35J25 Second order elliptic equations, boundary value problems 35B35 Stability of solutions of PDE 35A35 Theoretical approximation to solutions of PDE
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##### References:
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